Daubechies小波基波函数potential energy的有效数值求积
An efficient numerical quadrature for the calculation of the potential energy of wavefunctions expressed in the Daubechies wavelet basis
摘要：
提出了一种有效的数值求积方法，用于Daubechies小波基和尺度函数基赝势电子结构计算中势能的近似计算.我们的正交也适用于自适应空间分辨率的情况下。我们的理论误差估计得到了证实的数值试验计算的基态能量和波函数的谐振子在一维和无自适应分辨率。作为一个副产品，我们得到一个过滤器，在应用程序上的平滑函数的缩放函数系数，使近似网格值的这个功能。这也允许从波函数快速计算电荷密度。
英文摘要：
An efficient numerical quadrature is proposed for the approximate calculation of the potential energy in the context of pseudo potential electronic structure calculations with Daubechies wavelet and scaling function basis sets. Our quadrature is also applicable in the case of adaptive spatial resolution. Our theoretical error estimates are confirmed by numerical test calculations of the ground state energy and wave function of the harmonic oscillator in one dimension with and without adaptive resolution. As a byproduct we derive a filter, which, upon application on the scaling function coefficients of a smooth function, renders the approximate grid values of this function. This also allows for a fast calculation of the charge density from the wave function.
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